We consider the design of a control law K(s, θ) such that a set of trade-offs parameterized by a scalar θ are satisfied for a given LTI system. The trade-off is formulated as an optimization problem involving a weighted H∞ norm. Matrices of the state space representation of K(s, θ) have to be obtained as explicit functions of θ. This problem, close to the LPV control design, can be naturally fo...

We consider general non-convex optimal control problems. Many results for such problems rely on second-order sufficient optimality conditions. We propose a method to verify whether the second-order sufficient optimality conditions hold in a neighborhood of a numerical solution. This method is then applied to abstract optimal control problems. Finally, we consider an optimal control problem subj...

Modern databases have to cope with multi-dimensional queries. For efficient processing of these queries, query optimization relies on multi-dimensional selectivity estimation techniques. These techniques in turn typically rely on histograms. A core challenge of histogram construction is the detection of regions with a density higher than the ones of their surroundings. In this paper, we show th...

Robbins’s visionary 1951 paper can be seen as an exercise in binary classification, but also as a precursor to the outpouring of recent work on high-dimensional data analysis and multiple testing. It can also be seen as the birth of empirical Bayes methods. Our objective in the present note is to use this problem and several variants of it to provide a glimpse into the evolution of empirical Ba...

Reflectance spectroscopy obtained from a thermally treated silicon nitride carbon based ceramic matrix composite is used to quantity the oxidation products SiO2 and SiN. The data collection is described in detail in order to point out the potential biasing present in the data processing. A probability distribution is imposed on select model parameters, and then non-parametrically estimated. A n...

f -divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics and information theory such as Kullback-Leibler divergence, chi-squared divergence, squared Hellinger distance, total variation distance etc. In this paper, we study the problem of maximizing or minimizing an f -dive...

In many real world optimization problems, several optimization goals have to be considered in parallel. For this reason, there has been a growing interest in multi-objective optimization (MOO) in the past many years. Several new approaches have recently been proposed, which produced very good results. However, existing techniques have solved mainly problems of “low dimension”, i.e., with less t...

This paper is devoted to the simultaneous weight and stiffness optimization of two dimensional structures. The necessary optimality conditions are derived and the obtained optimality criterion is briefly explained. Based on the paradigm of cellular automata, a local rule is constructed which alleviates the well known problems of mesh dependency and checker-boarding in topological structural opt...

Purpose – The purpose of this paper is to present an algorithm for global optimization of high-dimensional real-parameter cost functions. Design/methodology/approach – This optimization algorithm, called differential ant-stigmergy algorithm (DASA), based on a stigmergy observed in colonies of real ants. Stigmergy is a method of communication in decentralized systems in which the individual part...

The objective of this module is to understand key problems that arise when moving from finite dimensional linear programs to infinite dimensional linear programs. Students are introduced to the theory of linear programming in 36900. In 36900 the primary focus is on linear and integer programs with a finite number of constraints and variables. However, there are many applications where the numbe...